If x is real then y is?

Algebra Level 3

If $y= 9^{x} - 3^{x} + 1$ , where $x$ can take any real value then $y$ takes:

none of these all real values greater than or equal to 0 all real values greater than or equal to 3/4 all real values

1 solution

Ashutosh Kumar
Jun 19, 2015

$y=3^{2x} - 3^{x} +1$

let $3^{x}=t$

$y= t^{2} -t +1$

Discriminant (D) = -3 < 0

coefficient of highest term is positive.

Hence y is always greater than 0 and has a minimum value equal to -D/4

-D/4 = 3/4

So y takes all real values greater than 3/4

After Tijmen Veltman's (Netherlands) report.

Hence the right answer should be "all real values greater than or equal to 3/4"